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Magnetic Field at Center of Arc Formula

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Field at Center of Arc is the magnetic field generated at the midpoint of the arc. It is influenced by the amount of current and the radius of the arc. Check FAQs

M arc = \frac{[Permeability-vacuum] \cdot i \cdot θ arc}{4 \cdot π \cdot r ring}

M_arc - Field at Center of Arc?i - Electric Current?θ_arc - Angle Obtained by Arc at Center?r_ring - Radius of Ring?[Permeability-vacuum] - Permeability of vacuum?π - Archimedes' constant?

Magnetic Field at Center of Arc Example

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Here is how the Magnetic Field at Center of Arc equation looks like with Values.

Here is how the Magnetic Field at Center of Arc equation looks like with Units.

Here is how the Magnetic Field at Center of Arc equation looks like.

1.8E-8 = \frac{1.3E-6 \cdot 0.1249 \cdot 0.5}{4 \cdot 3.1416 \cdot 0.006}

1.8E-8Wb/m² = \frac{1.3E-6 \cdot 0.1249A \cdot 0.5°}{4 \cdot 3.1416 \cdot 0.006m}

1.8E-8 = \frac{1.3E-6 \cdot 0.1249 \cdot 0.5}{4 \cdot 3.1416 \cdot 0.006}

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Magnetic Field at Center of Arc Solution

Follow our step by step solution on how to calculate Magnetic Field at Center of Arc?

FIRST Step Consider the formula

M arc = \frac{[Permeability-vacuum] \cdot i \cdot θ arc}{4 \cdot π \cdot r ring}

Next Step Substitute values of Variables

∴

M arc = \frac{[Permeability-vacuum] \cdot 0.1249A \cdot 0.5°}{4 \cdot π \cdot 0.006m}

Next Step Substitute values of Constants

∴

M arc = \frac{1.3E-6 \cdot 0.1249A \cdot 0.5°}{4 \cdot 3.1416 \cdot 0.006m}

Next Step Convert Units

∴

M arc = \frac{1.3E-6 \cdot 0.1249A \cdot 0.0087rad}{4 \cdot 3.1416 \cdot 0.006m}

Next Step Prepare to Evaluate

∴

M arc = \frac{1.3E-6 \cdot 0.1249 \cdot 0.0087}{4 \cdot 3.1416 \cdot 0.006}

Next Step Evaluate

∴

M arc = 1.81659686311709E-08T

Next Step Convert to Output's Unit

∴

M arc = 1.81659686311709E-08Wb/m²

LAST Step Rounding Answer

∴

M arc = 1.8E-8Wb/m²

Magnetic Field at Center of Arc Formula Elements

Variables

Constants

Field at Center of Arc

Field at Center of Arc is the magnetic field generated at the midpoint of the arc. It is influenced by the amount of current and the radius of the arc.

Symbol: M_arc

Measurement: Magnetic FieldUnit: Wb/m²

Note: Value can be positive or negative.

Formulas to find Field at Center of Arc

Electric Current

Electric Current is the flow of electric charge through a conductor. It is measured by the amount of charge passing a point in the conductor per unit time.

Symbol: i

Measurement: Electric CurrentUnit: A

Note: Value can be positive or negative.

Formulas to find Electric Current

Angle Obtained by Arc at Center

Angle Obtained by Arc at Center is the measure of the angle that the arc subtends at the circle's center. This angle depends on the length of the arc and the radius of the circle.

Symbol: θ_arc

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Angle Obtained by Arc at Center

Radius of Ring

The Radius of Ring is the distance from the center of the ring to any point on its circumference. It determines the size and shape of the ring.

Symbol: r_ring

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Ring

Permeability of vacuum

Permeability of vacuum is a fundamental physical constant that relates the magnetic field within a vacuum to the current producing that field.

Symbol: [Permeability-vacuum]

Value: 1.2566E-6

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other formulas in Magnetism category

Go Magnetic Field on Axis of Ring

B = \frac{[Permeability-vacuum] \cdot i \cdot {r ring}^{2}}{2 \cdot {({r ring}^{2} + d^{2})}^{\frac{3}{2}}}

Go Force between Parallel Wires

F 𝑙 = \frac{[Permeability-vacuum] \cdot I 1 \cdot I 2}{2 \cdot π \cdot d}

Go Field Inside Solenoid

B = \frac{[Permeability-vacuum] \cdot i \cdot N}{L solenoid}

Go Magnetic Field at Center of Ring

M ring = \frac{[Permeability-vacuum] \cdot i}{2 \cdot r ring}

How to Evaluate Magnetic Field at Center of Arc?

Magnetic Field at Center of Arc evaluator uses Field at Center of Arc = ([Permeability-vacuum]*Electric Current*Angle Obtained by Arc at Center)/(4*pi*Radius of Ring) to evaluate the Field at Center of Arc, Magnetic Field at Center of Arc formula is defined as a measure of the magnetic field strength at the center of an arc-shaped current-carrying wire, which is influenced by the permeability of the surrounding medium, the current flowing through the wire, and the angle subtended by the arc at its center. Field at Center of Arc is denoted by M_arc symbol.

How to evaluate Magnetic Field at Center of Arc using this online evaluator? To use this online evaluator for Magnetic Field at Center of Arc, enter Electric Current (i), Angle Obtained by Arc at Center (θ_arc) & Radius of Ring (r_ring) and hit the calculate button.

FAQs on Magnetic Field at Center of Arc

What is the formula to find Magnetic Field at Center of Arc?

The formula of Magnetic Field at Center of Arc is expressed as Field at Center of Arc = ([Permeability-vacuum]*Electric Current*Angle Obtained by Arc at Center)/(4*pi*Radius of Ring). Here is an example- 1.8E-8 = ([Permeability-vacuum]*0.1249*0.00872664625997001)/(4*pi*0.006).

How to calculate Magnetic Field at Center of Arc?

With Electric Current (i), Angle Obtained by Arc at Center (θ_arc) & Radius of Ring (r_ring) we can find Magnetic Field at Center of Arc using the formula - Field at Center of Arc = ([Permeability-vacuum]*Electric Current*Angle Obtained by Arc at Center)/(4*pi*Radius of Ring). This formula also uses Permeability of vacuum, Archimedes' constant .

Can the Magnetic Field at Center of Arc be negative?

Yes, the Magnetic Field at Center of Arc, measured in Magnetic Field can be negative.

Which unit is used to measure Magnetic Field at Center of Arc?

Magnetic Field at Center of Arc is usually measured using the Weber per Square Meter[Wb/m²] for Magnetic Field. Tesla[Wb/m²], Microtesla[Wb/m²], Megatesla[Wb/m²] are the few other units in which Magnetic Field at Center of Arc can be measured.

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Magnetic Field at Center of Arc Formula

Magnetic Field at Center of Arc Example

Magnetic Field at Center of Arc Solution

Magnetic Field at Center of Arc Formula Elements

Other formulas in Magnetism category

How to Evaluate Magnetic Field at Center of Arc?

FAQs on Magnetic Field at Center of Arc

Variable Name